In the attached file, I cannot find a non-manifold area in the object Cube.003. I've exported it as x3d and attempted to upload it to shapeways twice. Each time I get an error back saying the object is non-manifold. Is the .blend --> .x3d format conversion causing it to be non-manifold?

How do I find the inverted normals and fix them? I couldn't find any 'inverted normals' tutorial on this site. I cannot identify any inverted normals in Blender (unless I'm doing something wrong, which is very likely).

Are you sure that MiniMagics still allows editing? I downloaded and installed the program and it refers me to "Magic RP" to do all my editing/fixing. Or should I use minimagics just for finding the problems and edit the objects in Blender.

Another useful tip:
configure Blender to draw the face normals when editing the file.
That way you can see them in blender and in this case you would probably have to load/import the x3d file and check the results as well.

Go to Editing mode and open up the mesh editing buttons panel.
In the Mesh Tools More section there's a button labeled "Draw normals". Make sure it's selected/active.
The normals should point out from the "solid material area".

I use it all the time to make sure that the model won't spaz out when/if I add the SubSurf modifier.
(If you see a face normal where there should just be a face edge you have a face that is not visible to the eye but it effects the subsurf division quite clearly.. a common problem when a noob like me tries to extrude a face/edge and forgets to move it away from its original location)

The "Draw Vnormals" button does the same for the vertice normals, which may or may not be useful...